# FIND THE DISTANCE  BETWEEN TWO POINT USING FORMULA

## About "Find the Distance Between Two Points Using Formula"

Find the Distance Between Two Points Using Formula :

Here we are going to see some example problems to show finding distance between two points using formula.

## Find the Distance Between Two Points Using Formula - Practice questions

Question 1 :

Find the distance between the following pairs of points.

(i) (1, 2) and (4, 3)

Solution :

Distance between two points  =  √(x2 - x1)2 + (y2 - y1)2

=  √(4 - 1)2 + (2 - 3)2

=  √32 + (-1)2

=  √(9 + 1)

=  √10

(ii) (3, 4) and (– 7, 2)

Solution :

Distance between two points  =  √(x2 - x1)2 + (y2 - y1)2

=  √(-7 - 3)2 + (2 - 4)2

=  √(-10)2 + (-2)2

=  √(100 + 4)

=  √104

=  2 √26

(iii) (a, b) and (c, b)

Solution :

Distance between two points  =  √(x2 - x1)2 + (y2 - y1)2

=  √(c - a)2 + (b - b)2

=  √(c - a)2 + 02

=  (c - a)

(iv)  (3, -9) and (-2, 3)

Distance between two points  =  √(x2 - x1)2 + (y2 - y1)2

=  √(-2 - 3)2 + (3 - (-9))2

=  √(-5)2 + (3+9)2

=  √25 + 144

=  √169

=  13

Question 2 :

Determine whether the given set of points in each case are collinear or not.

(i) (7, –2),(5, 1),(3, 4)

Solution :

Let the given points be A (7, –2) B (5, 1) and C (3, 4)

Distance between the points A and B :

=  √(5 - 7)2 + (1 - (-2))2

=  √(-2)2 + (1+2)2

=  √4 + 9

=  √13

Distance between the points B and C :

=  √(3 - 5)2 + (4 - 1)2

=  √(-2)2 + (3)2

=  √4 + 9

=  √13

Distance between the points C and A :

=  √(3 - 7)2 + (4 - (-2))2

=  √(-4)2 + (6)2

=  √16 + 36

=  √52

=  2√13

√13 + √13  =  2√13

Hence the given points are collinear.

(ii) (a, –2), (a, 3), (a, 0)

Solution :

Let the given points be A (a, –2) B (a, 3) and C (a, 0)

Distance between the points A and B :

=  √(a - a)2 + (3 - (-2))2

=  √0 + (5)2

=  √0 + 25

=  √25

=  5

Distance between the points B and C :

=  √(a - a)2 + (0 - 3)2

=  √(0)2 + (3)2

=  √9

=  3

Distance between the points C and A :

=  √(a - a)2 + (0 - (-2))2

=  √(0)2 + (2)2

=  √4

=  2

BC + CA  =  AB

3 + 2  =  5

5  =  5

Hence the given points are collinear. After having gone through the stuff given above, we hope that the students would have understood, "Find the Distance Between Two Points Using Formula"

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